Changing several fractions with different denominators into fractions with the same mother equal to the original fraction is called the general fraction of fractions.
Note: General score guarantee (1) score is equal to the original score; (2) The denominators of the scores are equal.
2. Total score basis: the basic nature of the score.
3. The key to general division is to determine the simplest common denominator of several fractions.
Usually, the product of the highest power of all factors of each denominator is taken as the simplest common denominator.
According to the definition of general score and the simplest common denominator, scores are divided into:
The simplest common denominator is:, and then according to the basic properties of the fraction, multiply the numerator and denominator of the original fraction by an appropriate algebraic expression, so that all the denominators of the fraction are simplified to. The overall score is as follows:
Example 1 Comprehensive score:
( 1) , , ;
Analysis: Ask students to find the common denominator of fractions and ask, "How to solve the problem of different denominator coefficients?" Find the least common multiple according to the total score.
Solution: ∫ The simplest common denominator is 12x 2.
Summary: When the coefficients of all denominators are integers, the least common multiple of their coefficients is usually taken as the coefficient of the simplest common denominator.
Solution: ∫ The simplest common denominator is 10a2b2c2.
Students sum up the simplest common denominator.
The simplest common denominator in the general division of fractions can be summarized as: (1) take the least common multiple of denominator coefficient; (2) All factors based on letters should be taken; (3) The factor of the power of the same letter takes the largest exponent. Taking the product of these factors is the simplest common denominator.
Example 2 Comprehensive score:
Question: How to find the simplest common denominator for a general fraction whose denominator is polynomial?
The above is a monomial. For polynomials, we must first decompose the factors of polynomials, determine the factors contained in each denominator, and then determine the simplest common denominator.
Solution: The simplest common denominator is 2x(x+ 1)(x- 1).
Summary: When the denominator is a polynomial, the factor must be decomposed first.
Solution:
Factorization denominator: x2-4 = (x+2) (x-2) .4-2x =-2 (x-2).
The simplest common denominator is 2 (x+2) (x-2).
Ask students to sum up the general scores and general points:
The key to general division is to determine the simplest common denominator of several fractions, and the steps are as follows:
1. Factorize the denominator of each fraction;
2. Take the least common multiple of denominator coefficient;
3. All the letters or factors based on letters should be taken;
4. The factor with the same letter or the power of the factor with the letter takes the largest exponent;
5. Multiply all the above formulas to get the simplest common denominator;
6. Multiply the numerator and denominator of the atomic formula by an appropriate algebraic expression to simplify the denominator of each sub-formula to the simplest common denominator.
Exercise: 1, 2,3 Page 79
(3) class summary
1. Although general fractions and reduction are aimed at fractions, they are two opposite variants. Reduction is for one score, while general scores are for multiple scores. The approximate fraction is a simplified fraction, and the general fraction is a simplified fraction, thus unifying the denominator of the fraction.
2. Both general score and approximate score are deformed according to the basic properties of the score, and their similarity is to keep the value of the score unchanged.
3. The general denominator is written in the form of unexpanded continuous product, and the numerator multiplication is written in polynomial to prepare for further operation.